Markina I. Sub-Riemannian geometry on infinite dimensional manifolds, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract)
Speaker: Irina Markina
Title: Sub-Riemannian geometry on infinite dimensional manifolds
We start from the definition of an infinite-dimensional manifold with a specific choice of the underlying vector space for developing the smooth calculus. Then we define Riemannian and sub-Riemannian structures, and discuss the choice of a tool for studying geodesics on infinite-dimensional sub-Riemannian manifolds. We show that, similarly to the finite-dimensional case, there are two different, but not mutually disjoint classes of geodesics. We present geodesic equations for those classes of geodesics which is natural generalisations of classical Riemannian geodesics. We indicate possible applications to fluid mechanics and questions of controllability.